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The summary function in R starts with a five-number summary of the residuals. You should be getting comfortable with the output from statistical packages by now (having used regression in Excel and SAS). Example: If we have a regression equation \(Sales = \beta_0 + \beta_1 Advertising\) and the learned values of \(\beta_0\) and \(\beta_1\), then we can plug-in our expected advertising spend ( \(Advertising\)) and predict our sales for the coming period. This allows us to predict values of \(Y\) using the known values of \(X\). + \beta_n X_n\) can be solved for values of the explanatory variables \(X_i\). Prediction: The parameterized linear model \(Y = \beta_0 + \beta_1 X_1 +. A statistically insignificant value of \(\beta_1\) suggests that advertising has no impact on sales. Obviously, we want every dollar we spend on advertising to result in at least a dollar increase in sales, otherwise we are losing money on our advertising efforts. Example: If we have a regression equation \(Sales = \beta_0 + \beta_1 Advertising\), then we can use \(\beta_1\) to better understand the impact of our spending on advertising on sales. Root cause analysis: The size, direction (positive or negative), and statistical significance of each slope provides us with a better understanding of the factors that might cause variation in the value of the response variable \(Y\). The slopes learned by the linear regression algorithm can be used in two ways: We think of each \(\beta_i\) as the slope of the line (also called the “coefficient” or “parameter”). “Fitting a line” means finding values for each \(\beta_i\) so that the error (or “residual”) between the fitted line and the observed data is minimized. + \beta_n X_n\), where \(Y\) is the value of the response variable and \(X_i\) is the value of the explanatory variable(s). Recall that a linear model is of the form \(Y = \beta_0 + \beta_1 X_1 +. The lm function in R constructs-as its name implies-a linear model from data. 10.6 Standardized regression coefficients.9.1.3 Model quality and statistical significance.7.3.2 Using gmodel’s CrossTable Command.
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7 Gap Analysis with Categorical Variables.6.3.4 Equality of variance test (formula).6.3.3 Equality of variance test (pivoted columns).6.3.2 Equality of variance test (columns).6.2.2 Boxplots in base R (and formula notation).5.3 Recode According to List Membership.3.3.4 Relative frequency (more advanced).2.1.3 Load the tidyverse package into R.